Method for vibration measurement and diagnostics using single vibration measurement probe

ABSTRACT

A method which includes receiving a first signal from a first probe at a first location monitoring a rotating component, wherein the first location defines a cross-sectional plane that is perpendicular to the axis of rotation of the rotating component. The method further includes obtaining a vibration model and generating, by a computer processor, a virtual signal at a second location on the machine, where no second probe is present. The second location is in the same cross-sectional plane as the first location and is angularly offset by an angle from the first location. The method further includes performing a plurality of signal processing techniques based, at least in part, on the first signal and the virtual signal and transmitting a plurality of commands based, at least in part, on results of the plurality of signal processing techniques.

BACKGROUND

Equipment and machinery, and particularly those with rotationcomponents, may produce and/or experience vibrations. Probes may be usedat various locations on equipment or machinery to monitor thevibrations. The vibration signals from the probes may be used to monitorthe health of the equipment, detect component failures, and identifyareas where preventative maintenance may be taken. Some vibrationanalysis techniques require at least two probes to generate vibrationinformation such as phase angle, shaft orbit, bode plot, etc. Thetypical two probe system consists of two measurement devices usuallycalled X and Y interchangeably. They are located on the samecross-sectional plane with respect to the measured location and they areusually angularly separated by 60 to 120 degrees. In some instances, dueto physical or economical constraints, it is not possible to insert anduse two or more probes on a machine. In other words, in cases where onlyone probe may be used, potential vibration analysis techniques arelimited.

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used as an aid in limiting the scope ofthe claimed subject matter.

One or more embodiments disclosed herein generally relate to a methodwhich includes receiving a first signal from a first probe at a firstlocation monitoring a rotating component, wherein the first locationdefines a cross-sectional plane that is perpendicular to the axis ofrotation of the rotating component. The method further includesobtaining a vibration model and generating, by a computer processor, avirtual signal at a second location on the machine, where no secondprobe is present. The second location is in the same cross-sectionalplane as the first location and is angularly offset by an angle from thefirst location. The method further includes performing a plurality ofsignal processing techniques based, at least in part, on the firstsignal and the virtual signal and transmitting a plurality of commandsbased, at least in part, on results of the plurality of signalprocessing techniques.

One or more embodiments disclosed herein generally relate to methods andsystems to generate a virtual signal. The system having instructionsexecutable by a computer processor. The instructions includingfunctionality for receiving a first signal from a first probe at a firstlocation monitoring a rotating component, wherein the first locationlies in a cross-sectional plane that is perpendicular to the axis ofrotation of the rotating component. The instructions further includingfunctionality for obtaining a vibration model and generating a virtualsignal at a second location using the vibration model wherein the secondlocation lies in the same cross-sectional plane as the first location.The second location is angularly offset by an angle from the firstlocation. The instructions further including functionality forperforming a plurality of signal processing techniques based, at leastin part, on the first signal and the virtual signal. The instructionsfurther include functionality for transmitting a plurality of commandsto adjust the operation of the rotating component based, at least inpart, on the results of the plurality of signal processing techniques.

One or more embodiments disclosed herein generally relate to a system.The system includes a machine and a first vibration probe at a firstlocation disposed to monitor, at least, a rotating component of themachine. The first location defines a cross-sectional planeperpendicular to the axis of rotation of the rotating component. Thesystem further includes a vibration model. The system further includes acomputer communicably connected to the first vibration probe. Thecomputer includes one or more computer processors and a non-transitorycomputer readable medium storing instructions executable by a computerprocessor. The instructions include functionality for receiving a firstsignal from the first vibration probe and generating a virtual signal ata second location on the machine, wherein the second location lies inthe cross-sectional plane and is angularly offset by an angle from thefirst location. The instructions further include functionality forperforming a plurality of signal processing techniques based, at leastin part, on the first signal and the virtual signal. The instructionsfurther include functionality for transmitting a plurality of commandsto adjust the machine based, at least in part, on the results of theplurality of signal processing techniques.

Other aspects and advantages of the claimed subject matter will beapparent from the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

Specific embodiments of the disclosed technology will now be describedin detail with reference to the accompanying figures. Like elements inthe various figures are denoted by like reference numerals forconsistency.

FIG. 1 depicts a machine with rotating components, in accordance withone or more embodiments.

FIGS. 2A-C shows various vibration analysis plots, in accordance withone or more embodiments.

FIGS. 3A-C illustrates physical system models, in accordance with one ormore embodiments.

FIG. 4 depicts a system, in accordance with one or more embodiments.

FIG. 5 depicts a process, in accordance with one or more embodiments.

FIG. 6 depicts a process, in accordance with one or more embodiments.

FIG. 7 depicts a process, in accordance with one or more embodiments.

FIG. 8 depicts a flow chart, in accordance with one or more embodiments.

FIG. 9 depicts a neural network, in accordance with one or moreembodiments.

FIG. 10 depicts a system, in accordance with one or more embodiments.

DETAILED DESCRIPTION

In the following detailed description of embodiments of the disclosure,numerous specific details are set forth in order to provide a morethorough understanding of the disclosure. However, it will be apparentto one of ordinary skill in the art that the disclosure may be practicedwithout these specific details. In other instances, well-known featureshave not been described in detail to avoid unnecessarily complicatingthe description.

Throughout the application, ordinal numbers (for example, first, second,third) may be used as an adjective for an element (that is, any noun inthe application). The use of ordinal numbers is not to imply or createany particular ordering of the elements nor to limit any element tobeing only a single element unless expressly disclosed, such as usingthe terms “before”, “after”, “single”, and other such terminology.Rather, the use of ordinal numbers is to distinguish between theelements. By way of an example, a first element is distinct from asecond element, and the first element may encompass more than oneelement and succeed (or precede) the second element in an ordering ofelements.

Equipment and machinery may produce and/or be subjected to vibrations.For example, machines such as pumps, fans, turbines, and compressorscontain rotating components that cause vibrations. Plants or operatingfacilities using these machines may experience unscheduled upsets,downtime, or loss of performance with machine faults. It is generallybeneficial to an operating facility to run machines for longer periodsof time and reduce the amount of time that machines are out of use.Additionally, unexpected outages, which may cause a facility to reduceor stop production output, bear a high economic cost.

In general, to mitigate operational upsets and improve facilityreliability and performance, machines at an operating facility aremonitored and evaluated. Monitoring may be done with sensors or probesdesigned to measure physical quantities such as temperature or position.The probes may be embedded into the machines or may be external to themachines. By monitoring the machines, the health status of a machine maybe evaluated, the root cause of issues may be determined, and potentialfailure modes may be predicted. Predictive capability in an operatingfacility helps operators identify which equipment is most vulnerable tofailure and take preventative actions to reduce outages. In addition,strategically employed preventative maintenance increases the longevityand individual output of machines improving the production efficiency ofan operational facility.

Embodiments disclosed herein present a method for using a singlevibration measurement probe to generate a second “virtual” probe usingnumerical calculations and machine learning techniques. The invention inthis disclosure generates similar or better vibration information fromthe signal of only one physical probe to compute the second “virtual”probe using numerical methods, inferential methods, and machine learningtechniques.

FIG. 1 depicts a simplified example of a machine (100). The machine(100) of FIG. 1 contains a shaft (102) which rotates (104) about theshaft center (106). This machine (100) produces vibrations. A vibrationprobe (108) is attached to the machine (100). Many types of vibrationprobes (108) exist, but generally a vibration probe (108) measures thedisplacement (x), velocity ({dot over (x)}), or acceleration ({umlautover (x)}) of a component of a machine (100) or the machine (100) itselfin time. That is, a vibration probe (108) produces a time-seriesrepresenting the displacement (x), velocity ({dot over (x)}), oracceleration ({umlaut over (x)}) of an object at a sequence of discretesample times. Additionally, vibration probes (108) may include a speedsensor or tachometer, however, a speed sensor or tachometer is not astrict requirement. As an example, one type of vibration probe (108) isan Eddy-current sensor. Eddy-current sensors are non-contact sensorswhich generate a magnetic field and measure the relative displacement(x) of an object. Other vibration probes (108) may include, but are notlimited to: strain gauges; gyroscopes; accelerometers; and microphones.

FIG. 1 illustrates one vibration probe (108) attached to the simplemachine (100); namely, a first probe (X). If a second vibration probe(108) were attached to the machine (100) it would be referenced as asecond probe (Y). In the example of FIG. 1 , the first probe (X) issituated to measure the vibrations (through displacement (x), velocity({dot over (x)}), or acceleration ({umlaut over (x)}) of the shaft(102). Typically, in the case of a first probe (X) and a second probe(Y), the first probe (X) and the second probe (Y) are located on thesame cross-sectional plane of the machine (100) but are angularly offsetby an angle θ. The angle θ is usually between 60 and 180 degrees.Vibration probes (108) are accompanied by control equipment (109). Thecontrol equipment (109) may include additional instruments, cables,junction boxes, power supplies, communication and data interfaces,networking capabilities, and control modules.

As previously stated, a vibration probe (108) produces a time-seriessignal. As illustrated in FIG. 1 , the first probe (X) outputs a firstsignal (114) representing the measured time-history and strength of thevibrations (displacement (x), velocity ({dot over (x)}), or acceleration({umlaut over (x)})) of the shaft (102) proximate the location of thefirst probe (X).

One with ordinary skill in the art will appreciate that the machine(100) and vibration probes (108) as shown in FIG. 1 may be configured ina variety of ways according to the specific needs of an operatingfacility or plant. For example, the machine (100) need not includerotating components to produce or be subject to vibrations. As such, themachine (100) and arrangement of vibration probes (108) as shown in FIG.1 are non-limiting.

The signal of a vibration probe (108), or the signals of many vibrationprobes (108), may be processed and analyzed, independently or together,to further represent the state, condition, or properties of a machine(100). Analyses and methods to transform vibration probe (108) signalsto useful information are herein described as signal processingtechniques. Signal processing techniques may include, but are notlimited to: the application of a Fourier transform to convert the signalfrom the time-domain to the frequency-domain; time- or frequency-basedsignal filtering; autoregressive averages; and high-order statistics.Some signal processing techniques require two or more vibration probe(108) signals.

Often, the result of signal processing techniques may be displayedgraphically. FIGS. 2A-2C demonstrate plots that may be constructed todisplay information acquired through the analysis of vibration probe(108) signals. Specifically, FIG. 2A depicts an orbit plot (202). Asillustrated, an orbit plot (202) is constructed by simultaneouslyplotting the signals from two vibration probes (108) disposed atdifferent locations on a machine on orthogonal axes; for example,signals from a first probe (X) and a second probe (Y). Note, that if theoffset angle θ (110) between the first probe (X) and the second probe(Y) is not 90 degrees (π/4 radians), additional processing is requiredto form an orbit plot (202). An orbit plot (202) provides a graphicalrepresentation of shaft (102) motion. An orbit plot (202) may be used todetect excessive shaft (102) movement and indicate when a shaft (102)may contact and damage other components of the machine (100). Generally,perturbations or malfunctions in machinery with rotating shafts may bedetected through evaluation of an orbit plot (202). Additionally, orbitplot (202) shape is related to machine (100) health and condition.

FIG. 2B demonstrates a Bode plot (204). A Bode plot (204) displays thephase response (206) and amplitude response (208) of a vibration probe(108) signal as a function of the shaft (102) rotational speed. The Bodeplot (204) is particularly useful for evaluating machine (100) behaviorand health during transient periods; such as the startup and shut-downof a machine (100). A Bode plot (204) may be displayed as a polar plot(not shown) wherein the Bode plot (204) data is presented in a Nyquistformat. Bode plots (204) may also be useful in identifying critical orresonant rotational speeds of a shaft (102).

FIG. 2C depicts a waterfall plot (210). A waterfall plot (210) may alsobe referenced as a cascade plot or a spectrogram in the literature. Awaterfall plot (210) may plot the frequency spectra (212) of a vibrationprobe (108) signal as a function of time. A vibration probe (108) signalmay be decomposed into a plurality of individual signals — each with anassociated frequency. The frequency spectra (212) represent the strengthof decomposed single-frequency signals. Again, the frequency spectra may(212) be evaluated to determine the health of a machine (100) or thecondition and state of components of a machine (100). For example, anabrupt change in the frequency spectra (212) in time may indicate adamaged component, such as a bearing.

Many signal processing techniques exist, and there are many ways tographically display information acquired through a signal processingtechnique. As such, it is emphasized that the graphical representationsand associated signal processing techniques shown in FIGS. 2A-2C areprovided as an example and are not all-inclusive. Additional signalprocessing techniques and graphical displays may include: shaft (102)vibration phase angle; shaft (102) wave form; shaft center (104)location plot; and frequency spectrum analysis for vibration probes(108).

One with ordinary skill in the art will appreciate that the fact thatnot all signal processing techniques and graphical representations areenumerated herein does not limit the scope of the present disclosure.Because signal processing techniques transform one or more vibrationprobe (108) signals into useful information regarding the state,condition, and health of a machine (100), the results of signalprocessing techniques may be evaluated to determine the best course ofaction for a machine (100), or machinery, of an operating facility. Forexample, upon evaluation of a waterfall plot (210) it may be determinedthat a component of a machine (100) has sustained wear and is nearingfailure. Consequently, an action to replace the component of the machine(100) may be scheduled. By identifying and predicting which machine(100), or components of machines (100), are faulty or nearing failure,preventative actions may be performed to promote optimal production inan operating facility and mitigate against unscheduled upsets anddowntime.

In some instances, the vibrations of a machine (100) may be modeled by aphysical system model (300). As an example, FIG. 3A depicts an idealizedone degree of freedom (1-dof) system (302). The 1-dof system (302) is adiscretized model of a dynamic system and relates the movement of a massto external forces. The dynamic system is modeled using a lumped singlepoint mass (304). The position of the mass at any instance in time isdenoted by x(t) (306), where the position is measured relative to adatum (308). The stored, or internal, energy of the dynamic system ismodeled as a spring (310) which has an associated spring stiffness, k.Energy is dissipated from the dynamic system through a damper (312)wherein the damping strength is indicated by a damping coefficient, C.For example, a viscous damper (312) may represent the dissipation ofenergy outside of the dynamic system as heat. The dynamic system may besubjected to a time-dependent external force represented as a forcingfunction, ƒ(t) (314). Physical systems of greater complexity, or higherdegrees of freedom, may be represented by physical system models (300)with many springs (310), dampers (312), and masses (304). Complexphysical system models (300) may be constructed through a combinationand arrangement of many 1-dof systems (302).

The 1-dof system (302) of FIG. 3A may be mathematically modeled as

m{umlaut over (x)}+C{dot over (x)}+kx=ƒ(t),  (1)

where m is the mass (304) of the system, C is the damper (312)coefficient, k is the spring (310) stiffness, ƒ(t) is the forcingfunction (314), and {umlaut over (x)}, {dot over (x)}, and x are theinstantaneous acceleration, velocity, and displacement of the mass(304), respectively, relative to a datum (308). As previously stated,vibration probes (108) measure displacement (x), velocity ({dot over(x)}), or acceleration ({umlaut over (x)}). In general, measurement ofany one of displacement (x), velocity ({dot over (x)}), or acceleration({umlaut over (x)}) is sufficient to determine the remaining two throughapplication of a derivative and/or an integral. For example, givendisplacement (x), velocity ({dot over (x)}) and acceleration ({umlautover (x)}) may be determined. As such, a vibration probe (108) providesa lot of information with respect to the mathematical model of a dynamicsystem. It is noted that some caveats may apply when converting betweendisplacement (x), velocity ({dot over (x)}) and acceleration ({umlautover (x)}); the signals may require pre-processing and/or smoothing, anddepending on the frequencies present in the signal, a minimum samplingrate may be required.

FIG. 3B depicts another simplified viewpoint of a machine (100). Here, arotating shaft (102) contains a disc (318) with an associated mass, m.The disc is circumvented by a stator (320). The shaft (102) is supportedby fluid-film bearings (322) on the ends of the shaft (322). Thefluid-film bearing end-supported shaft (316) may be described with aphysical system model (300). FIG. 3C shows the two degree of freedom(2-dof) system (324) which describes the machine (100) of FIG. 3B. FIG.3C is a cross-section of the simple machine (100) of FIG. 3B proximateone of the fluid-filled bearings (322). As shown, the shaft (102) issupported within the bearing housing (326). The two degrees of freedomof this physical system model (300) are defined by a coordinate systemwith Y axis and a Z axis (325). Like the physical system model (300) ofFIG. 3A, various springs (310) and dampers (312) are used to modelstored energy and dissipated energy, respectively, of the dynamicsystem.

The 2-dof system (324) of FIG. 3C may be mathematically modeled with thefollowing equations:

mÿ+C{dot over (y)}+ky=F _(y) +F _(by) +mu _(im)ω² cos(ωt)−mg

m{umlaut over (z)}+Cż+kz=F _(z) +F _(bz) +mu _(im)ω² sin(ωt).  (2)

In the above equations, co is the angular speed of the shaft (102), k isthe shaft stiffness, C is the shaft damping coefficient, u_(im) is theunbalance eccentricity, and g is the acceleration due to gravity. ÿ,{dot over (y)}, and y are the instantaneous acceleration, velocity, anddisplacement, respectively, relative to the Y axis. Likewise, {umlautover (z)}, ż, and z are the instantaneous acceleration, velocity, anddisplacement, respectively, relative to the Z axis. F_(y) and F_(z) arerubbing forces generated due to the interaction of the disc (318) andstator (320). Expressions for F_(y) and F_(z) may be derived withsimplifying assumptions, however, they are omitted here for brevity.F_(by) and F_(bz) are bearing reaction forces and are given as

$\begin{matrix}{\begin{bmatrix}F_{by} \\F_{bz}\end{bmatrix} = {{\begin{bmatrix}k_{yy} & k_{yz} \\k_{zy} & k_{zz}\end{bmatrix}\begin{bmatrix}y \\z\end{bmatrix}} - {\begin{bmatrix}C_{yy} & C_{yz} \\C_{zy} & C_{zz}\end{bmatrix}\begin{bmatrix}\overset{˙}{y} \\\overset{˙}{z}\end{bmatrix}}}} & (3)\end{matrix}$

where the spring (310) stiffnesses and damping coefficients are shown inFIG. 3C.

On some machines (100), due to physical or economical constraints, it isonly possible to use a single vibration probe (108). For example, theconstruction of the machine (100) or its placement within an operatingfacility may deny access to a vibration probe (108). In other instances,the machine (100) may not have physical space available for a vibrationprobe (108) and/or the associated control equipment (109). Further, thecost of additional vibration probes (108) may be burdensome limiting themonitoring of a machine (100) to a single vibration probe (108). Aspreviously stated, some signal processing techniques require signalsfrom two or more vibration probes (108). Consequently, in cases where amachine (100) is monitored by a single vibration probe (108), theavailable signal processing techniques are limited. Because signalprocessing techniques transform the vibration probe (108) signals intouseful information which may be graphically represented and/or evaluatedto determine the health, state, and condition of a machine (100), alimitation on the available signal processing techniques likewiserestricts the evaluation of the machine (100).

Embodiments disclosed herein relate to a method of generating one ormore virtual vibration signals from a single vibration probe (108) usingmachine learning (ML) and/or numerical techniques. In accordance withone or more embodiments, a machine (100) may include one or more virtualvibration measuring systems. For example, the machine (100) of FIG. 1 ,due to a constraint, only allows for a single vibration probe (108); afirst probe (X). The first probe (X) resides at a first location on themachine (100). The first probe (X) outputs a first signal (114)representing the measured time-history and strength of the vibrations(displacement (x), velocity ({dot over (x)}), or acceleration ({umlautover (x)}) of the shaft (102) proximate the first location. A virtualprobe (V) is depicted as residing at a second location. The virtualprobe (V) outputs a virtual signal (112). The virtual probe (V) is notphysically present at the machine (100) and is only illustrated on FIG.1 to promote understanding. The first location and the second locationreside on the same cross-sectional plane of the machine (100) but areangularly offset by an angle ϕ (116). The virtual signal (112)represents the signal that would be output by a vibration probe (108) ifa vibration probe (108) was present at the second location. Using thevirtual signal (112) and the first signal (114), more signal processingtechniques are available to analyze the vibration signals. Inparticular, a virtual vibration measuring system may include a controlsystem or other computer device that acquires sensor measurements frommultiple sensors (e.g. vibration probes (108)) with respect to a machine(100) or component of a machine (100). A virtual vibration measuringsystem, with knowledge of, at least, the first location of a first probe(X) on a machine (100), may determine the vibration signal (i.e. virtualsignal (112)) at a second location, where the second location is on thesame cross-sectional plane as the first probe (X) but angularly offset,without using a second probe (Y) (i.e. a physical sensor). In someembodiments, for example, a virtual vibration measuring system uses aphysical system model (300) to determine a respective virtual signal(112). Examples of physical system models may include orifice those seenin FIGS. 3A and 3C, which are mathematically represented by EQs. 1 and2-3, respectively. In some embodiments, for example, a virtual vibrationmeasuring system uses a machine-learned model (300) to determine arespective virtual signal (112).

Turning to FIG. 4 , FIG. 4 shows a schematic diagram in accordance withone or more embodiments. As shown in FIG. 4 , a virtual vibrationmeasuring system (e.g., virtual vibration measuring system A (400)) mayinclude a control system (402), a machine (100), one or more vibrationprobes (108) (e.g. a first probe (X), a second probe (Y), a third probe(Z), etc.), one or more signals received from the vibration probes (108)(e.g. a first signal (114), a second signal (402), a third signal(404)), one or more angular offsets (408), and a vibration model (406).In the case with multiple probes, as in FIG. 4 , the virtual vibrationmeasuring system A (400) allows for the generation of one or morevirtual signals (V) for each physical probe (first probe (X), etc.). Forexample, in a machine (100) with a shaft (102), a first probe (X) and asecond probe (Y) may be disposed along a shaft at two different axiallocations. As such, the first probe (X) may be used, with the virtualvibration measuring system A (400) to generate a first virtual signal onthe same cross-sectional plane as the first probe (X) but angularlyoffset by an angle ϕ_(X) listed in the angular offsets (408). Likewise,the second probe (Y) may be used with the virtual vibration measuringsystem A (400) to generate a second virtual signal on the samecross-sectional plane as the second probe (Y) (which is at a differentlocation along the axis of the shaft (102) than the first probe (X)) butangularly offset by an angle ϕ_(Y) indicated by the angular offsets(408).

In some embodiments, a control system (401) in the virtual vibrationmeasuring system includes a vibration model (406). The vibration model(406) may consist of a physical system model (300), a machine-learnedmodel, or both.

Machine learning, broadly defined, is the extraction of patterns andinsights from data. The phrases “artificial intelligence”, “machinelearning”, “deep learning”, “statistical learning”, “fitting”, and“pattern recognition” are often convoluted, interchanged, and usedsynonymously throughout the literature. This ambiguity arises becausethe field of “extracting patterns and insights from data” was developedsimultaneously and disjointedly among a number of classical arts likemathematics, statistics, and computer science. Herein, machine learningis defined to specifically comprise techniques for determining unknownparameters in a model. Moreover, for consistency, the term machinelearning, or machine-learned, will be adopted herein, however, oneskilled in the art will recognize that the concepts and methods detailedhereafter are not limited by this choice of nomenclature.

Machine-learned model types that may be used in the vibration model(406) may include, but are not limited to, neural networks, randomforests, generalized linear models, long short term memory (LSTM)networks, transformers, genetic algorithms, optimization methods, andBayesian regression. Machine-learned model types are usually associatedwith additional “hyperparameters” which further describe the model. Forexample, hyperparameters providing further detail about a neural networkmay include, but are not limited to, the number of layers in the neuralnetwork, choice of activation functions, inclusion of batchnormalization layers, and regularization strength. The selection ofhyperparameters surrounding a model is referred to as selecting themodel “architecture”.

In particular, a vibration model (406) may describe one or more physicalcriteria or conditions for determining a virtual vibration signal. Forexample, the vibration model (406) may specify various boundaryconditions or physical system coefficients. In some embodiments, amachine-learned model directly relating a physical signal (e.g. thefirst signal (114)) to a virtual signal (114) may be trained usingphysics-based constraints (e.g. a regularization term that penalizesdivergence from a physical system model (300)). In some embodiments, asmachine-learned model comprising a fitting or optimization routine maybe used to estimate any unknown parameters in the physical system model(300).

With respect to control systems (401), a control system may includehardware and/or software that monitors and/or operates equipment, suchas on a machine (100) or for machinery at an operations facility. Inparticular, a control system (401) may be coupled to facility equipmentand sensors to collect data throughout a facility. For example, facilityequipment may include various hardware components, such as, pumps,valves, and compressors among various other types of hardwarecomponents. Examples of sensors may include pressure sensors,temperature sensors, torque sensors, weight sensors, vibration probes,accelerometers, etc. In some embodiments, a control system (401) mayinclude a programmable logic controller that may control the state (e.g.“on” or “off”, operational speed, etc.) of one or more machines (100).In some embodiments, the control system (401) may activate warningalarms, emergency stops and/or various hardware components throughout afacility. Thus, a programmable logic controller may be a ruggedizedcomputer system with functionality to withstand vibrations, extremetemperatures, wet conditions, and/or dusty conditions, such as thosepotentially found in an operational facility. Furthermore, a controlsystem may be a computer system similar to the computer system (1002)described in FIG. 10 and the accompanying description.

In some embodiments, a control system includes a distributed controlsystem (DCS). A distributed control system may be a computer system formanaging various processes at a facility using multiple control loops.As such, a distributed control system may include various autonomouscontrollers (such as remote terminal units (RTUs)) positioned atdifferent locations throughout the facility to manage operations andmonitor processes. Likewise, a distributed control system may include nosingle centralized computer for managing control loops and otheroperations. With respect to an RTU, an RTU may include hardware and/orsoftware, such as a microprocessor, that connects sensors and/oractuators using network connections to perform various processes in theautomation system.

By generating one or more virtual signals from a single vibration probe(108) (or multiple vibration probes (108) at disposed on differentcross-sectional planes), no limitation is placed on the available signalprocessing techniques and machine (100) health, condition, and statemonitoring is greatly improved. Improved health, state, and conditionmonitoring reduces uncertainty about which course of action, if any,should be taken on a machine (100).

In accordance with one or more embodiments, a process of generating avirtual signal (112) is shown in FIG. 5 . As seen, there is anundetermined physical system model (502) which models the dynamicresponse of a machine (100). The physical system model (300) is said tobe undetermined because not all of the parameters of the physical systemmodel (300) are known. That is, the undetermined physical system model(502) contains known parameters (504) and unknown parameters (503). Inone or more embodiments, the unknown parameters (503) may include spring(310) stiffnesses or damper (312) coefficients. A first signal (114) ata first location on the machine (100) is collected. The first signal(114), with knowledge of the undetermined physical system model (502) isprocessed by a machine-learned model (505) to determine the unknownparameters (503). In other words, the machine-learned model (404)outputs determined unknown parameters (506), where a value for eachunknown parameter (503) has been determined.

Keeping with FIG. 5 , the determined unknown parameters (506) may beused in the physical system model (300), for example, one of thephysical system models (300) of FIG. 3 . For clarity, a physical systemmodel (300) which uses the determined unknown parameters (406) isreferred to as a determined physical system model (508). The determinedphysical system model (508) possesses all the parameters necessary tomodel the dynamic system. The first signal (114) and the offset angle ϕ(116) between the first location and the second location are used withthe determined physical model (508) to generate the virtual signal(112). The offset angle ϕ (116) may be chosen by a user, effectivelyplacing the virtual probe (V) at any location on the machine (100) alongthe same cross-sectional plane as the first probe (X).

In accordance with one or more embodiments, the machine-learned model(505) may generate a virtual signal (118) from a first signal (114) andoffset angle ϕ (116) without referencing a physical system model (300).As shown in FIG. 6 , the machine-learned model (505) may be configuredto directly accept a first signal (114). The first signal (114) comesfrom a physical probe on a machine (100) of interest and has a knownlocation. The machine-learned model (404) outputs the virtual signal(118) from a virtual probe (V) such that a second physical probe is notrequired on the machine (100). The location of the virtual probe (V) onthe machine of interest is dictated relative to the location of thephysical probe and is defined by the offset angle ϕ (116). In someembodiments, the offset angle ϕ (116) is an input of the machine-learnedmodel (404) as shown in FIG. 6 , whereas in other embodiments the offsetangle ϕ (116) is a configuration parameter of the machine-learned model(505).

Regardless of whether the machine-learned model (505) references aphysical system model (300) or not, the machine-learned model (505) willneed to be trained. Training a machine-learned model (505), generally,consists of providing the model with training data, wherein the trainingdata contains both the planned input to the model and associatedexpected output of the model. For example, in accordance with one ormore embodiments, the training data may be received from one or moremachines (100) equipped with at least two vibration probes (108). Theinput may consist of a first signal (114) from a first probe (X) and anangle θ dictating the angular offset of a second probe (Y) from thefirst probe (X). The output data consists of a second signal from thesecond probe (Y) such that the desired output of the machine-learnedmodel is the second signal given the first signal (114). In thisexample, the machine-learned model (505) may be trained to associate thesecond signal with the first signal (114) such that the second signal isno longer required. As such, the output of the machine-learned model(505) may be thought of as a virtual signal (112) since a second probe(Y) is not required to generate a second signal.

In some embodiments, training data is collected from vibration probes(108) on one or more machines (100) equipped with two or more vibrationprobes (108) angularly offset at various angles θ where the machines(100) may be subjected to known forces or forcing functions. The imposedforces or forcing functions may be designed, and/or generated, to mimica wide variety of scenarios encountered with machine use, such asimbalance, misalignment, and rub. In this way, a robust set of trainingdata may be collected so that the resulting trained machine-learnedmodel (505) is readily applicable to many machine vibration scenarios.

In some embodiments, a physical system model (300) is used to describe amachine (100). The vibrational response of the machine (100) may besimulated by applying a variety of forcing functions, or forces, to thephysical system model (300). The simulated vibrational response isrepresentative of the signal that would be recorded by a vibration probe(108). Using the physical system model (300) and an applied forcingfunction or force, the signal of one or more vibration probes (108)(e.g. a first probe (X) and a second probe (Y)) may be simulated andrecorded. In some embodiments, the first probe (X) may be a physicalvibration probe (108) such that only the second probe (Y) signal needsto be simulated. The simulated vibrational responses of the probes maybe used as training data to train a machine-learned model (505) togenerate the response of one probe (e.g. the second probe (Y)) given theresponse of another probe (e.g. the first probe (X)). In someembodiments, a simulated signal may be validated using a physicalvibration probe (108) or a physically-acquired signal may be used with asimulated signal. Training data may be generated for different physicalsystem models (300) (e.g. different value for spring constants, etc.). Amachine-learned model (505) should be trained using training datagenerated using a physical system model (300) that is representative ofthe machine (100) on which the machine-learned model (505) will beapplied. Once trained, using training data from a physical system modelrepresentative of a machine (100), the machine-learned model (505) maybe applied to the machine (100) with only a single vibration probe (108)to generate a second signal from a virtual probe (V).

More details surrounding training a machine-learned model (505) areprovided below under the context of a neural network.

In accordance with one or more embodiments, FIG. 7 depicts anothermethod to collect training data and train a combination ofmachine-learned models. As seen in FIG. 7 , training data is collectedfrom one or more machines (100) with at least two vibration probes (108)and a speed sensor or tachometer. In some embodiments, a speed sensor ortachometer is not used. For the present example, a machine (100) isequipped with a first probe (X) and a second probe (Y). The first probe(X) outputs a first signal (114) and the second probe outputs a secondsignal (701). For clarity, FIG. 7 depicts the first signal (114) andsecond signal (701) as a time-series where the value of the signals at agiven time t is given as X(t) and Y(t), respectively. In someembodiments, the time t may index a complete revolution (or cycle) (e.g.a rotating shaft (102)) such that X(t) and Y(t) represent a sequence ofvalues (i.e. X(t) is the recorded signal for one cycle and X(t+1) is therecorded signal for the next cycle). A machine-learned model A (703) istrained using only the first signal (114). Machine-learned model A (703)is trained to predict the value of the first signal (114) at a time(t+1) given the value of the first signal (114) at time t. Once trained,machine-learned model A (703) produces a prediction for X(t+1) given aninput of X(t). For clarity, the prediction of machine-learned model A(703) is designated as X′(t+1). The prediction of machine-learned modelA (703) is compared to the actual value of the first signal (114) ateach timestep (t+1) to compute an error, ε(t+1). A machine-learned modelB (705) is trained to predict the value of the second signal (701) at atime t, Y(t). Again, for clarity, the prediction of machine-learnedmodel B (705) is designated as Y′(t). During training, machine-learnedmodel B (705) receives the value of the first signal (114) at time t,X(t), along with the error of machine-learned model A (703), ε(t+1), andthe angular offset of the two vibration probes (108), θ(707), the valueof the second signal (701) at a time t, Y(t), and, in some embodiments,the value of the tachometer. Thus, once trained, machine-learned model A(703) and machine-learned model B (705) may be used in coordination tooutput a signal for a virtual probe (V) using a first signal (114) froma first probe (X), a tachometer value (in some embodiments), and anindication of the angular offset between the virtual probe (V) and thefirst probe (X).

In accordance with one or more embodiments, FIG. 8 depicts a flow chart(800) outlining the general method of generating a virtual signal (V)monitoring a rotating component, where the rotating component may bepart of a machine (100), performing signal processing techniques usingthe virtual signal (V), and adjusting the rotating component and/ormachine (100) based on the results of the signal processing techniques.As shown in block 802 a first signal (114) from a first probe (X) at afirst location is received. The first location lies in a cross-sectionalplane where the cross-sectional plane is perpendicular to the axis ofrotation of the rotating component. The first probe (X) is a physicalprobe. The first signal (114) is the time-history of the strength ofvibrations, measuring either displacement (x), velocity ({dot over(x)}), or acceleration ({umlaut over (x)}) proximate the first location.As depicted in block 806, a vibration model (406) is obtained. Thevibration model (406) may be a machine-learned model (505) and themachine-learned model (505) may be informed or constrained by a physicalsystem model (300). As shown in block 808, a virtual signal (112) isgenerated at a second location. The second location is located in thesame cross-sectional plane as the first location but angularly offsetfrom the first location. As described in block 810, signal processingtechniques may be applied to the first signal (114) and the virtualsignal (112). It is emphasized that signal processing techniques thatrequire at least two vibration probe (108) signals (112, 114) may beperformed. Because the signal processing techniques are not limited tothose that work on a single vibration probe (108) signal, moreinformation regarding the state, condition, and health of the rotatingcomponent and/or machine (100) may be extracted. The signal processingtechniques may determine quantities such as shaft vibration phase angle,shaft orbit plot and wave form, shaft centerline location, vibrationfrequency spectrum for horizontal and vertical locations of vibrations,etc. More specifically, for example, an orbit plot (202) may be createdusing signal processing techniques when the rotating component is ashaft (102). The orbit plot (202) may be evaluated to detect excessiveshaft (102) movement and indicate when a shaft (102) may contact anddamage other components of the machine (100). Moreover, the orbit plot(202) may be evaluated to detect perturbations or malfunctions in themachine (100). As shown in block 812, using the results of the signalprocessing techniques, commands regarding adjustments to be made to therotating component and/or machine are transmitted. Based on thecondition and state of the machine (100), an appropriate action may betaken. Actions that may be taken on a rotating component and/or amachine (100) include, but are not limited to: no adjustment required;shutting down the operation of the component and/or machine (100);replacing the rotating component and/or machine (100); repairing therotating component and/or machine (100); and performing maintenanceoperation on the rotating component and/or the machine (100).

As an example, consider an air compressor equipped with only a singlevibration probe (108). A single signal from a single probe does notprovide sufficient information to predict failures in advance, butrather a single probe can only provide a late indication of major damageto/within the air compressor. As such, it is not possible to plan, orotherwise decide on, an action to take on such a machine. Using thetechniques of the present disclosure, a virtual signal may be generated,and two-signal vibration analyses may be applied. These two-signalvibration analyses can detect vibration signatures known to beassociated with machine issues, or burgeoning machine issues, such asinternal misalignments, and poor bearing lubrication. With an issuedetected, an operator may take an action, such as scheduling a repair,before any damage to a machine becomes irreversible or irreparable.

While the various blocks in FIG. 8 are presented and describedsequentially, one of ordinary skill in the art will appreciate that someor all of the blocks may be executed in different orders, may becombined or omitted, and some or all of the blocks may be executed inparallel. Furthermore, the blocks may be performed actively orpassively.

Embodiments of the present disclosure may provide at least one of thefollowing advantages. It is noted that because the vibration probes(108) have associated locations, evaluation of the results of signalprocessing techniques may further specify the location of failure oranomaly in a machine (100). By identifying, or predicting, the faultycomponent of a machine (100), the time required to diagnose and inspecta machine (100), and subsequently repair, maintain, or replace a machine(100) is reduced. Degradation of machine (100) performance may beidentified early. Information regarding early performance degradationand prediction of failures may be used to prevent catastrophic failures;either by adjusting operating conditions or by taking an action on themachine. By preventing a catastrophic failure, the economically costlyevent of an unscheduled operating facility outage may be avoided.Additionally, embodiments of the present disclosure eliminate humanerrors in diagnosing issues within a machine (100).

As stated, many machine-learned model (505) types are available. Inaccordance with one or more embodiments, the selected machine-learnedmodel (505) type is a neural network. A diagram of a neural network isshown in FIG. 9 . At a high level, a neural network (900) may begraphically depicted as being composed of nodes (902), where here anycircle represents a node, and edges (904), shown here as directed lines.The nodes (902) may be grouped to form layers (905). FIG. 9 displaysfour layers (908, 910, 912, 914) of nodes (902) where the nodes (902)are grouped into columns, however, the grouping need not be as shown inFIG. 9 . The edges (904) connect the nodes (902). Edges (904) mayconnect, or not connect, to any node(s) (902) regardless of which layer(905) the node(s) (902) is in. That is, the nodes (902) may be sparselyand residually connected. A neural network (900) will have at least twolayers (905), where the first layer (908) is considered the “inputlayer” and the last layer (914) is the “output layer”. Any intermediatelayer (910, 912) is usually described as a “hidden layer”. A neuralnetwork (900) may have zero or more hidden layers (910, 912) and aneural network (900) with at least one hidden layer (910, 912) may bedescribed as a “deep” neural network or as a “deep learning method”. Ingeneral, a neural network (900) may have more than one node (902) in theoutput layer (914). In this case the neural network (900) may bereferred to as a “multi-target” or “multi-output” network.

Nodes (902) and edges (904) carry additional associations. Namely, everyedge is associated with a numerical value. The edge numerical values, oreven the edges (904) themselves, are often referred to as “weights” or“parameters”. While training a neural network (900), numerical valuesare assigned to each edge (904). Additionally, every node (902) isassociated with a numerical variable and an activation function.Activation functions are not limited to any functional class, buttraditionally follow the form

A=ƒ(Σ_(i∈(incoming))[(node value)_(i)(edge value)_(i)]),

where i is an index that spans the set of “incoming” nodes (902) andedges (904) and ƒ is a user-defined function. Incoming nodes (902) arethose that, when viewed as a graph (as in FIG. 9 ), have directed arrowsthat point to the node (902) where the numerical value is beingcomputed. Some functions for ƒ may include the linear function ƒ(x)=x,sigmoid function

${{f(x)} = \frac{1}{1 + e^{- x}}},$

and rectified linear unit function ƒ(x)=max(0, x), however, manyadditional functions are commonly employed. Every node (902) in a neuralnetwork (900) may have a different associated activation function.Often, as a shorthand, activation functions are described by thefunction ƒ by which it is composed. That is, an activation functioncomposed of a linear function ƒ may simply be referred to as a linearactivation function without undue ambiguity.

When the neural network (900) receives an input, the input is propagatedthrough the network according to the activation functions and incomingnode (902) values and edge (904) values to compute a value for each node(902). That is, the numerical value for each node (902) may change foreach received input. Occasionally, nodes (902) are assigned fixednumerical values, such as the value of 1, that are not affected by theinput or altered according to edge (904) values and activationfunctions. Fixed nodes (902) are often referred to as “biases” or “biasnodes” (906), displayed in FIG. 9 with a dashed circle.

In some implementations, the neural network (900) may containspecialized layers (905), such as a normalization layer, or additionalconnection procedures, like concatenation. One skilled in the art willappreciate that these alterations do not exceed the scope of thisdisclosure.

As noted, the training procedure for the neural network (900) comprisesassigning values to the edges (904). To begin training the edges (904)are assigned initial values. These values may be assigned randomly,assigned according to a prescribed distribution, assigned manually, orby some other assignment mechanism. Once edge (904) values have beeninitialized, the neural network (900) may act as a function, such thatit may receive inputs and produce an output. As such, at least one inputis propagated through the neural network (900) to produce an output.Recall, that a given data set will be composed of inputs and associatedtarget(s), where the target(s) represent the “ground truth”, or theotherwise desired output. The neural network (900) output is compared tothe associated input data target(s). The comparison of the neuralnetwork (900) output to the target(s) is typically performed by aso-called “loss function”; although other names for this comparisonfunction such as “error function”, “misfit function”, and “costfunction” are commonly employed. Many types of loss functions areavailable, such as the mean-squared-error function, however, the generalcharacteristic of a loss function is that the loss function provides anumerical evaluation of the similarity between the neural network (900)output and the associated target(s). The loss function may also beconstructed to impose additional constraints on the values assumed bythe edges (904), for example, by adding a penalty term, which may bephysics-based, or a regularization term. For example, the neural network(900), or more generally a machine-learned model (505), may quantify anduse violations of a physical system model (300) to regularize the modelduring training. Such a process is often referred to as“physics-informed machine learning” or a “physics-informed neuralnetwork” (PINN) in the literature. Generally, the goal of a trainingprocedure is to alter the edge (904) values to promote similaritybetween the neural network (900) output and associated target(s) overthe data set. Thus, the loss function is used to guide changes made tothe edge (904) values, typically through a process called“backpropagation”.

While a full review of the backpropagation process exceeds the scope ofthis disclosure, a brief summary is provided. Backpropagation consistsof computing the gradient of the loss function over the edge (904)values. The gradient indicates the direction of change in the edge (904)values that results in the greatest change to the loss function. Becausethe gradient is local to the current edge (904) values, the edge (904)values are typically updated by a “step” in the direction indicated bythe gradient. The step size is often referred to as the “learning rate”and need not remain fixed during the training process. Additionally, thestep size and direction may be informed by previously seen edge (904)values or previously computed gradients. Such methods for determiningthe step direction are usually referred to as “momentum” based methods.

Once the edge (904) values have been updated, or altered from theirinitial values, through a backpropagation step, the neural network (900)will likely produce different outputs. Thus, the procedure ofpropagating at least one input through the neural network (900),comparing the neural network (900) output with the associated target(s)with a loss function, computing the gradient of the loss function withrespect to the edge (904) values, and updating the edge (904) valueswith a step guided by the gradient, is repeated until a terminationcriterion is reached. Common termination criteria are: reaching a fixednumber of edge (904) updates, otherwise known as an iteration counter; adiminishing learning rate; noting no appreciable change in the lossfunction between iterations; reaching a specified performance metric asevaluated on the data or a separate hold-out data set. Once thetermination criterion is satisfied, and the edge (904) values are nolonger intended to be altered, the neural network (900) is said to be“trained”.

FIG. 10 further depicts a block diagram of a computer system (1002) usedto provide computational functionalities associated with the algorithms,methods, functions, processes, flows, and procedures as described inthis disclosure, according to one or more embodiments. The illustratedcomputer (1002) is intended to encompass any computing device such as aserver, desktop computer, laptop/notebook computer, wireless data port,smart phone, personal data assistant (PDA), tablet computing device, oneor more processors within these devices, or any other suitableprocessing device, including both physical or virtual instances (orboth) of the computing device. Additionally, the computer (1002) mayinclude a computer that includes an input device, such as a keypad,keyboard, touch screen, or other device that can accept userinformation, and an output device that conveys information associatedwith the operation of the computer (1002), including digital data,visual, or audio information (or a combination of information), or aGUI.

The computer (1002) can serve in a role as a client, network component,a server, a database or other persistency, or any other component (or acombination of roles) of a computer system for performing the subjectmatter described in the instant disclosure. In some implementations, oneor more components of the computer (1002) may be configured to operatewithin environments, including cloud-computing-based, local, global, orother environment (or a combination of environments).

At a high level, the computer (1002) is an electronic computing deviceoperable to receive, transmit, process, store, or manage data andinformation associated with the described subject matter. According tosome implementations, the computer (1002) may also include or becommunicably coupled with an application server, e-mail server, webserver, caching server, streaming data server, business intelligence(BI) server, or other server (or a combination of servers).

The computer (1002) can receive requests over network (1030) from aclient application (for example, executing on another computer (1002)and responding to the received requests by processing the said requestsin an appropriate software application. In addition, requests may alsobe sent to the computer (1002) from internal users (for example, from acommand console or by other appropriate access method), external orthird-parties, other automated applications, as well as any otherappropriate entities, individuals, systems, or computers.

Each of the components of the computer (1002) can communicate using asystem bus (1003). In some implementations, any or all of the componentsof the computer (1002), both hardware or software (or a combination ofhardware and software), may interface with each other or the interface(1004) (or a combination of both) over the system bus (1003) using anapplication programming interface (API) (1012) or a service layer (1013)(or a combination of the API (1012) and service layer (1013). The API(1012) may include specifications for routines, data structures, andobject classes. The API (1012) may be either computer-languageindependent or dependent and refer to a complete interface, a singlefunction, or even a set of APIs. The service layer (1013) providessoftware services to the computer (1002) or other components (whether ornot illustrated) that are communicably coupled to the computer (1002).The functionality of the computer (1002) may be accessible for allservice consumers using this service layer. Software services, such asthose provided by the service layer (1013), provide reusable, definedbusiness functionalities through a defined interface. For example, theinterface may be software written in JAVA, C++, or other suitablelanguage providing data in extensible markup language (XML) format oranother suitable format. While illustrated as an integrated component ofthe computer (1002), alternative implementations may illustrate the API(1012) or the service layer (1013) as stand-alone components in relationto other components of the computer (1002) or other components (whetheror not illustrated) that are communicably coupled to the computer(1002). Moreover, any or all parts of the API (1012) or the servicelayer (1013) may be implemented as child or sub-modules of anothersoftware module, enterprise application, or hardware module withoutdeparting from the scope of this disclosure.

The computer (1002) includes an interface (1004). Although illustratedas a single interface (1004) in FIG. 10 , two or more interfaces (1004)may be used according to particular needs, desires, or particularimplementations of the computer (1002). The interface (1004) is used bythe computer (1002) for communicating with other systems in adistributed environment that are connected to the network (1030).Generally, the interface (1004) includes logic encoded in software orhardware (or a combination of software and hardware) and operable tocommunicate with the network (1030). More specifically, the interface(1004) may include software supporting one or more communicationprotocols associated with communications such that the network (1030) orinterface's hardware is operable to communicate physical signals withinand outside of the illustrated computer (1002).

The computer (1002) includes at least one computer processor (1005).Although illustrated as a single computer processor (1005) in FIG. 10 ,two or more processors may be used according to particular needs,desires, or particular implementations of the computer (1002).Generally, the computer processor (1005) executes instructions andmanipulates data to perform the operations of the computer (1002) andany algorithms, methods, functions, processes, flows, and procedures asdescribed in the instant disclosure.

The computer (1002) also includes a memory (1006) that holds data forthe computer (1002) or other components (or a combination of both) thatcan be connected to the network (1030). The memory may be anon-transitory computer readable medium. For example, memory (1006) canbe a database storing data consistent with this disclosure. Althoughillustrated as a single memory (1006) in FIG. 10 , two or more memoriesmay be used according to particular needs, desires, or particularimplementations of the computer (1002) and the described functionality.While memory (1006) is illustrated as an integral component of thecomputer (1002), in alternative implementations, memory (1006) can beexternal to the computer (1002).

The application (1007) is an algorithmic software engine providingfunctionality according to particular needs, desires, or particularimplementations of the computer (1002), particularly with respect tofunctionality described in this disclosure. For example, application(1007) can serve as one or more components, modules, applications, etc.Further, although illustrated as a single application (1007), theapplication (1007) may be implemented as multiple applications (1007) onthe computer (1002). In addition, although illustrated as integral tothe computer (1002), in alternative implementations, the application(1007) can be external to the computer (1002).

There may be any number of computers (1002) associated with, or externalto, a computer system containing computer (1002), wherein each computer(1002) communicates over network (1030). Further, the term “client,”“user,” and other appropriate terminology may be used interchangeably asappropriate without departing from the scope of this disclosure.Moreover, this disclosure contemplates that many users may use onecomputer (1002), or that one user may use multiple computers (1002).

Although only a few example embodiments have been described in detailabove, those skilled in the art will readily appreciate that manymodifications are possible in the example embodiments without materiallydeparting from this invention. Accordingly, all such modifications areintended to be included within the scope of this disclosure as definedin the following claims. In the claims, means-plus-function clauses areintended to cover the structures described herein as performing therecited function and not only structural equivalents, but alsoequivalent structures. Thus, although a nail and a screw may not bestructural equivalents in that a nail employs a cylindrical surface tosecure wooden parts together, whereas a screw employs a helical surface,in the environment of fastening wooden parts, a nail and a screw may beequivalent structures. It is the express intention of the applicant notto invoke 35 U.S.C. § 112(f) for any limitations of any of the claimsherein, except for those in which the claim expressly uses the words‘means for’ together with an associated function.

What is claimed is:
 1. A method, comprising: receiving a first signalfrom a first probe at a first location monitoring a rotating component,wherein the first location lies in a cross-sectional plane that isperpendicular to an axis of rotation of the rotating component;obtaining a vibration model; generating, by a computer processor, avirtual signal at a second location using the vibration model, whereinthe second location lies in the cross-sectional plane and the secondlocation is angularly offset by an angle from the first location;performing a plurality of signal processing techniques based, at leastin part, on the first signal and the virtual signal; and transmitting aplurality of commands to adjust an operation of the rotating componentbased, at least in part, on results of the plurality of signalprocessing techniques.
 2. The method of claim 1, wherein the rotatingcomponent is part of a machine.
 3. The method of claim 2, furthercomprising: evaluating the machine based, at least in part, on resultsof the plurality of signal processing techniques; and performing one ormore actions on the machine based on evaluation of the machine.
 4. Themethod of claim 3, wherein the one or more actions comprise repairingthe machine.
 5. The method of claim 1, further comprisingpre-processing, by the computer processor, the first signal.
 6. Themethod of claim 1, wherein the vibration model comprises amachine-learned model.
 7. The method of claim 6, wherein themachine-learned model is trained using a third signal and a fourthsignal, wherein the third signal is obtained by a physical probemonitoring a machine while being subjected to a variety of forcingfunctions and the fourth signal is generated using a physical systemmodel describing the machine and the third signal.
 8. The method ofclaim 6, wherein the machine-learned model is trained using a fifthsignal and a sixth signal, wherein the fifth and sixth signals areobtained using physical probes monitoring a machine with rotatingequipment, wherein the physical probes are located on a secondcross-sectional plane which is perpendicular to the axis of rotation ofthe machine and the physical probes are separated by an offset angle. 9.The method of claim 1, wherein the plurality of signal processingtechniques comprises creating an orbit plot.
 10. A non-transitorycomputer readable medium storing instructions executable by a computerprocessor, the instructions comprising functionality for: receiving afirst signal from a first probe at a first location monitoring arotating component, wherein the first location lies in a cross-sectionalplane that is perpendicular to an axis of rotation of the rotatingcomponent; obtaining a vibration model; generating a virtual signal at asecond location using the vibration model, wherein the second locationlies in the cross-sectional plane and the second location is angularlyoffset by an angle from the first location; performing a plurality ofsignal processing techniques based, at least in part, on the firstsignal and the virtual signal; and transmitting a plurality of commandsto adjust an operation of the rotating component based, at least inpart, on results of the plurality of signal processing techniques. 11.The non-transitory computer readable medium of claim 10, wherein therotating component is part of a machine.
 12. The non-transitory computerreadable medium of claim 11, further comprising instructions for:evaluating the machine based, at least in part, on results of theplurality of signal processing techniques; and determining one or moreactions to be performed on the machine based on evaluation of themachine.
 13. The non-transitory computer readable medium of claim 10,further comprising instructions for pre-processing the first signal. 14.The non-transitory computer readable medium of claim 10, wherein thevibration model comprises a machine-learned model.
 15. Thenon-transitory computer readable medium of claim 14, wherein themachine-learned model is trained using a third signal and a fourthsignal, wherein the third signal is obtained by a physical probemonitoring a machine while being subjected to a variety of forcingfunctions and the fourth signal is generated using a physical systemmodel describing the machine and the third signal.
 16. Thenon-transitory computer readable medium of claim 14, wherein themachine-learned model is trained using a fifth signal and a sixthsignal, wherein the fifth and sixth signals are obtained using physicalprobes monitoring a machine with rotating equipment, wherein thephysical probes are located on a second cross-sectional plane which isperpendicular to the axis of rotation of the machine and the physicalprobes are separated by an offset angle.
 17. A system, comprising: amachine; a first vibration probe at a first location disposed tomonitor, at least, a component of the machine, wherein the component ofthe machine rotates about an axis of rotation, and wherein the firstlocation defines a cross-sectional plane perpendicular to the axis ofrotation; a vibration model; and a computer communicably connected tothe first vibration probe and comprises: one or more computerprocessors, and a non-transitory computer readable medium storinginstructions executable by a computer processor, the instructionscomprising functionality for: receiving a first signal from the firstvibration probe; generating a virtual signal at a second location on themachine using the vibration model, wherein the second location lies inthe cross-sectional plane defined by the first location and is angularlyoffset by an angle from the first location; performing a plurality ofsignal processing techniques based, at least in part, on the firstsignal and the virtual signal; and transmitting a plurality of commandsto adjust the machine based, at least in part, on results of theplurality of signal processing techniques.
 18. The system of claim 17,further comprising instructions for: pre-processing the first signal,evaluating the machine based, at least in part, on results of theplurality of signal processing techniques; and determining one or moreto be performed actions on the machine based on evaluation of themachine.
 19. The system of claim 18, wherein the one or more actionscomprise repairing the machine.
 20. The system of claim 17, wherein thevibration model comprises a machine-learned model.